Criticality and Continuity of Explosive Site Percolation in Random Networks

This Letter studies the critical point as well as the discontinuity of a class of explosive site percolation in Erd\"{o}s and R\'{e}nyi (ER) random network. The class of the percolation is implemented by introducing a best-of-m rule. Two major results are found: i). For any specific $m$, the critical percolation point scales with the average degree of the network while its exponent associated with $m$ is bounded by -1 and $\sim-0.5$. ii). Discontinuous percolation could occur on sparse networks if and only if $m$ approaches infinite. These results not only generalize some conclusions of ordinary percolation but also provide new insights to the network robustness.Comment: 5 pages, 5 figure

Ab-initio simulation and experimental validation of beta-titanium alloys

In this progress report we present a new approach to the ab-initio guided bottom up design of beta-Ti alloys for biomedical applications using a quantum mechanical simulation method in conjunction with experiments. Parameter-free density functional theory calculations are used to provide theoretical guidance in selecting and optimizing Ti-based alloys with respect to three constraints: (i) the use of non-toxic alloy elements; (ii) the stabilization of the body centered cubic beta phase at room temperature; (iii) the reduction of the elastic stiffness compared to existing Ti-based alloys. Following the theoretical predictions, the alloys of interest are cast and characterized with respect to their crystallographic structure, microstructure, texture, and elastic stiffness. Due to the complexity of the ab initio calculations, the simulations have been focused on a set of binary systems of Ti with two different high melting bcc metals, namely, Nb and Mo. Various levels of model approximations to describe mechanical and thermodynamic properties are tested and critically evaluated. The experiments are conducted both, on some of the binary alloys and on two more complex engineering alloy variants, namely, Ti-35wt.%Nb-7wt.%Zr-5wt.%Ta and a Ti-20wt.%Mo-7wt.%Zr-5wt.%Ta.Comment: 23 pages, progress report on ab initio alloy desig

Effect of cell density on thrombin binding to a specific site on bovine vascular endothelial cells.

We studied thrombin binding to proliferating and confluent endothelial cells derived from bovine vascular endothelium. [125]thrombin was incubated with nonconfluent or confluent endothelial cells and both the total amount bound and the amount linked in a 77,000-dalton thrombin-cell complex were determined. Approximately 230,000 molecules of thrombin bound per cell in nonconfluent cultures compared to 12,800 molecules per cell in confluent cultures. Approximately 67,7000 thrombin molecules were bound in an apparently covalent complex, Mr = 77,000, with each cell in sparse cultures, whereas only 4,600 thrombin molecules per cell were bound in this complex with confluent cultures. Similar studies with [125I]thrombin and endothelial cells derived from bovine cornea revealed no difference either in the total amount of thrombin bound or in the amount bound in the 77,000-dalton complex using sparse or confluent cultures. When confluent vascular endothelial cultures were wounded, additional cellular binding sites for the 77,000-dalton complex with thrombin appeared within 24 h. A 237% increase in the amount of thrombin bound to these sites was induced by a wound which resulted in a 20% decrease in cell number in the monolayer. There was no significant increase in thrombin binding to other cellular sites at 24 h. These experiments provide evidence that the first change in thrombin binding after injury is an increase in the cellular sites involved in the 77,000-dalton complex, and suggest that thrombin binding to endothelial cells may be important in the vascular response to injury

Single Spin Asymmetry in Lepton Angular Distribution of Drell-Yan Processes

We study the single spin asymmetry in the lepton angular distribution of Drell-Yan processes in the frame work of collinear factorization. The asymmetry has been studied in the past and different results have been obtained. In our study we take an approach different than that used in the existing study. We explicitly calculate the transverse-spin dependent part of the differential cross-section with suitable parton states. Because the spin is transverse, one has to take multi-parton states for the purpose. Our result agrees with one of the existing results. A possible reason for the disagreement with others is discussed.Comment: Typos corrected. Conclusions unchange

Quantum Effects in Neural Networks

We develop the statistical mechanics of the Hopfield model in a transverse field to investigate how quantum fluctuations affect the macroscopic behavior of neural networks. When the number of embedded patterns is finite, the Trotter decomposition reduces the problem to that of a random Ising model. It turns out that the effects of quantum fluctuations on macroscopic variables play the same roles as those of thermal fluctuations. For an extensive number of embedded patterns, we apply the replica method to the Trotter-decomposed system. The result is summarized as a ground-state phase diagram drawn in terms of the number of patterns per site, $\alpha$, and the strength of the transverse field, $\Delta$. The phase diagram coincides very accurately with that of the conventional classical Hopfield model if we replace the temperature T in the latter model by $\Delta$. Quantum fluctuations are thus concluded to be quite similar to thermal fluctuations in determination of the macroscopic behavior of the present model.Comment: 34 pages, LaTeX, 9 PS figures, uses jpsj.st

Colour in visualisation for computational fluid dynamics

Colour is used in computational fluid dynamic (CFD) simulations in two key ways. First it is used to visualise the geometry and allow the engineers to be confident that the model constructed is a good representation of the engineering situation. Once an analysis has been completed, colour is used in post-processing the data from the simulations to illustrate the complex fluid mechanic phenomena under investigation. This paper describes these two uses of colour and provides some examples to illustrate the key visualisation approaches used in CFD